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5th Grade Math Worksheet - A Parent's Guide

Many educators, politicians, and parents believe the instruction of mathematics in the United States is in crisis mode, and
has been for some time. Indeed, recent test results show that 29 other countries on math
testing scores outperformed American 15-year-olds.
1 To help counter this crisis, educational, civic, and business leaders worked together
to develop the Common Core State Standards (CCSS).

The goal of Common Core is to establish consistent, nationwide guidelines of what children should be learning each school
year, from kindergarten all the way through high school, in English and math. Though CCSS
sets forth these criteria, states and school districts are tasked with developing curricula
to meet the standards.

The 2014-15 school year will be important for Common Core as the standards are fully implemented in many states remaining
states of the 43 (and the District of Columbia) that have embraced their adoption. CCSS has
its advocates as well as its critics, and the debate on its merits has become more pronounced
in recent months. Irrespective of the political differences with Common Core, its concepts
are critical for students because the standards help with understanding the foundational
principles of how math works. This guide steers clear of most of the controversy surrounding
CCSS and primarily focuses upon the math your fifthgrader will encounter.

Common Core Standards

A stated objective of Common Core is to standardize academic guidelines nationwide. In other words, what fifth-graders are
learning in math in one state should be the same as what students of the same age are learning
in another state. The curricula may vary between these two states, but the general concepts behind
them are similar. This approach is intended to replace wildly differing guidelines among different
states, thus eliminating (in theory) inconsistent test scores and other metrics that gauge student
success.

An increased focus on math would seem to include a wider variety of topics and concepts being taught at every grade level,
including fourth grade. However, CCSS actually calls for fewer topics at each grade level. The
Common Core approach (which is clearly influenced by so-called “Singapore Math”—an educational
initiative that promotes mastery instead of memorization) goes against many state standards,
which mandate a “mile-wide, inch-deep” curriculum in which children are being taught so much
in a relatively short span of time that they aren’t effectively becoming proficient in the concepts
they truly need to succeed at the next level. Hence, CCSS works to establish an incredibly thorough
foundation not only for the math concepts in future grades, but also toward practical application
for a lifetime.

For fifth grade, Common Core’s focus includes fluency in adding and subtracting numbers up to 1,000,000. Multiplication and
division of whole numbers are emphasized, as well as problem solving, with a goal of eventually
applying the concepts they learn at school to situations outside the classroom. Ultimately, the
focus will enable children to develop rigor in real-life situations by developing a base of conceptual
understanding and procedural fluency.

Critical Areas of Focus

CCSS doesn’t overload fifth-graders with too many new concepts, but it does greatly expand on some topics that were taught
the previous year. However, this level’s focus does plant the seeds for the much more advanced
math students will encounter in middle school. If anything, students, and parents, can consider
fifth grade as a preview of what’s ahead—working hard this year will create a strong foundation
and good habits for the future. Here are the three critical areas that Common Core brings to
fifth-grade math:

Fractions

Common Core covers fractions extensively in fifth grade, and it doesn’t let up for fifth. Students this year, will become
fluent in adding and subtracting fractions and get their first chance to solve equations with
two different denominators (e.g., 1/5 + 3/7). Fifth-graders will also begin to multiply fractions
and receive some limited instruction on dividing them (mostly a whole number divided by a fraction—15
÷ 1/3, for example).

Division, Decimals

Division, with divisors of two or more digits, is the last of the four basic operations in which students will achieve multiple-digit
fluency. Once fifth-graders can add, subtract, multiply, and divide big numbers (as well as use
estimation), the attention will turn toward decimals—how they work, are notated, and compared;
how they relate to fractions; and how they are used in the four basic operations to the hundredths
place.

Volume

Most of the Common Core geometry to this point has been two-dimensional— polygons, angles, lines,
and so forth. Fifth grade introduces a third dimension, with an emphasis on volume, on 1x1x1
cubes as a unit of measurement, and on how addition and multiplication tie into these concepts.

Overview of Topics

From the three critical areas of focus discussed in the previous section, Common Core also further clarifies the skills fifth-graders
should know by the end of the school year. For example, the fluency requirement at this level
is multi-digit multiplication—students should be proficient in multiplying big numbers before
they move on to sixth grade. The five topics presented here, taken directly from CCSS itself,2
include some specifics on what kids will be taught in Grade 5.

Operations and Algebraic Thinking

Write and interpret numerical expressions.
Parentheses and brackets in mathematical expressions—for example, 2 x (5+7)—as
well as the order of operations are introduced. Also, students will be taught to write simple
expressions that record calculations, as well as to interpret numerical expressions without
necessarily reaching an answer.

Analyze patterns and relationships.
Fifth-graders will be challenged to generate two numerical patterns given two rules. In a hint of the algebra that will come
in future grades, students will graph ordered pairs generated from these patterns onto a
coordinate plane.

Number Operations in Base 10

Understand the place value system.
Place value has been taught before; here, it is reemphasized with an additional focus on understanding that a digit in a
certain place is 10 times more of what it would be in the place to its right (e.g., 800÷10=80)
and 1/10th of what it would be to its left (800x10=8,000). This is important because students
will also be taught place values of decimals to thousandths, as well as place value operations
with decimals (e.g., 0.63÷0.07=9, the same answer as if you multiplied the original equation
by 100 to get 63÷7). Also, powers of 10 and exponents are introduced.

Numbers and Operations: Fractions

Use equivalent fractions as a strategy to add and subtract fractions.
Before this year, fractional equations featured the same denominator for each part of the problem. In fifth grade, the denominators
will differ, and students will need to determine equivalent fractions to solve problems.
For example, 1/3 + 1/7 = 7/21 + 3/21 = 10/21.

Build fractions from unit fractions by applying and extending previous understandings of
operations on whole numbers.
Essentially, this is learning how to add and subtract fractions with like denominators. Fractions multiplied by a whole number
will also be taught at this level.

Apply and extend previous understandings of multiplication and division to multiply and divide
fractions.
Operations involving fractions really ramp up when students get to multiplication. They will learn that all division is essentially
a fraction in which the numerator is divided by the denominator. Students won’t quite divide
fractions by fractions yet, but they will divide whole numbers by unit fractions (fractions
with 1 as the numerator). Word problems using all these areas of focus will be emphasized,
and students will be encouraged to use a visual fraction model to help reach an answer (for
example, with 2/3 x 4, imagine four pie charts split in three with two pieces in each shaded;
simply count up the shaded parts to get 8/3). Finally, these fraction concepts will be tied
into volume.

Measurement and Data

Solve problems involving measurement and conversion of measurements from a larger unit to
a smaller unit. This includes measurements of length, weights, and time. Furthermore,
word problems are emphasized—making change, figuring out elapsed time, computing perimeter,
and so on.

Represent and interpret data.
Students will learn how to interpret and create their own line plots

Geometric measurement: Understand concepts of angle and measure angles.
Protractors will be employed to help provide an understanding of angles of different
degrees.

Measurement and Data

Represent and interpret data.
Students will introduce fractions to line plots, which isn’t as simple as it might seem (after all, 2/8 would be plotted
before 1/3 because the former is less)

Geometric measurement: Understand concepts of volume and relate volume to multiplication
and to addition.
The concept of a cubic unit is introduced to offer a standard measurement for volume. Students will also learn how to compute
and compare the volume of a rectangular prism (height x width x length).

Geometry

Graph points on the coordinate plane to solve real-world and mathematical problems.
In another definite precursor to algebra, students will use graphs to plot points using X and Y axes on a coordinate system
in the first quadrant of the plane.

Classify two-dimensional figures into categories based on their properties.
Just because volume has been introduced doesn’t mean two-dimensional shapes have been forgotten. Students will learn how
to understand the attributes that shapes can display and the relationships between those
attributes. For example, a quadrilateral has four sides, a rhombus has four sides, and, therefore,
a rhombus is a quadrilateral.

The Truth About CCSS and Performance

Common Core aims to improve educational performance and standardize what students should learn at every grade in preparation
for a lifetime of application, but it does not set curricula, nor does it direct how teachers should
teach. As with any educational reform, some teachers, schools, and school districts will struggle
with CCSS, some will seamlessly adapt, and some will thrive. As a parent, your responsibility is
to monitor what your fifth-grader is learning, discover what is working or isn’t working for your
child, and to communicate with his or her teacher—and to accept that your children’s math instruction
does differ from what you learned when you were younger, or even what they might have learned last
year. The transition can be a little daunting for parent and student alike, but that’s not a product
of the standard itself. Common Core simply takes a new, more pointed approach to improving the quality
of math instruction in this country.

The Benefits

As previously mentioned, CCSS decreases the number of topics students learn at each grade. However, the remaining topics
are covered so extensively that the chances a child will master the corresponding skills increase.
An analogy to this approach is comparing two restaurants. One restaurant has a varied menu with dozens
of items; the other only serves hamburgers, fries, and milk shakes. The quality of the food at the
first restaurant may vary upon the cooks’ experience, the multitude of ingredients required for so
many offerings, and the efficiency (or lack thereof) of the staff. Because the second restaurant
only serves three items, mastering those three items efficiently should result in an excellent customer
experience. That’s not to say the first restaurant won’t succeed (because many do), but there’s always
a chance that something on the menu won’t live up to the business’s own expectations.

By reducing the number of math topics taught, Common Core helps ensure students are truly ready for what comes next. Given
the attention given to the included concepts, more practical applications and alternate operations
of the math can be explored.

Coinciding with the reduction of topics is an emphasis on vigor—achieving a “deep command” of the math being taught. Students
will be challenged to understand the concepts behind mathematical operations rather than just resorting
to rote memorization and processes to get a right answer. Speed and accuracy are still important;
kids won’t be getting away that easily from flash cards and quizzes that increase fluency. Moreover,
Common Core places even additional emphasis on practical application—after all, the math kids learn
now, will be important when they become adults, even if they never have to think about prime numbers
or symmetrical lines in their day-to-day lives.

Finally, CCSS links standards from grade to grade so that the skills learned at one level translate into the tools they need
to learn at the next level. This coherence would seem an obvious educational approach, but often,
there is no link—students are taught a skill in fifth grade that might not be used (and might have
to be retaught) until sixth. Each new concept in Common Core is an extension of a previous, already
learned concept.

Math Practices to Help Improve Performance

In addition to the grade-specific standards it sets forth, Common Core also emphasizes eight “Standards of Mathematical Practice”
that teachers at all levels are encouraged to develop in their students.3 These eight practices,
designed to improve student performance, are described here, with added information on how they apply
to fifth-graders.

Make sense of problems and persevere in solving them
Students explain the problem to themselves and determine ways they can reach a solution. Then, they work at the problem until
it’s solved. By fifth grade, students will have seen their share of word problems and other
tasks that require deeper thinking than just using a simple algorithm. Despite that experience,
kids at this age can still become flustered with a more complex problem. Common Core encourages
fifth-graders to apply what they have learned toward a solution, even if the process doesn’t
result in a correct answer. The process is key; the answers will eventually follow.

Reason abstractly and quantitatively
Students decontextualize and contextualize problems. By decontextualizing, they break down the problem into anything other
than the standard operation. By contextualizing, they apply math into problems that seemingly
have none. Fifth-graders, for example, who are decontextualizing might draw pie pieces
to help with adding fractions with different denominators; students who are contextualizing
may use the years of math they have already learned to help solve a word problem.

Construct viable arguments and critique the reasoning of others
Students use their acquired math knowledge and previous results to explain or critique their work or the work of others.
By fifth grade, many kids can offer step-by-step reasoning of how they solved a problem.
Subtracting fractions with different denominators, for example, requires several steps;
fifth-graders will be challenged to explain each step en route to an answer, or come
to a conclusion on where they went wrong.

Model with mathematics
This is just like it sounds: Students use math to solve real-world problems. Fifth-graders should be able to start recognizing
math in the world around them, even without looking for it. Eventually, they will start applying
the math they learn in school to real-life situations, and vice versa. Sometimes, thinking
of a math problem as something they would encounter outside the classroom helps them develop
strategies toward a solution.

Use appropriate tools strategically
Another self-explanatory practice: Students learn and determine which tools are best for the math problem at hand. Fifth-graders
working with threedimensional shapes might use cubes as a unit of measurement, or they might
simply measure an object with a ruler and multiply the results to get an answer. Either way,
what’s important is that they are deciding what will work best in their quest for a solution.

Attend to precision
Students strive to be exact and meticulous—period. With the inclusion of decimals and multi-digit operations, one small error
can throw off an entire process. Fifth-graders must take care in their work and be ready
to doublecheck their answers if necessary. And if a student is struggling, he or she should
either take steps to figure out what’s gone wrong or ask for help.

Look for and make use of structure
Students will look for patterns and structures within math and apply these discoveries to subsequent problems. For example,
fifth-graders might be asked to solve 253 ÷ 1/2. If they have recognized that dividing any
number by 1/2 is simply doubling the number, they can easily add 253 to 253 for an answer
of 506

Look for and express regularity in repeated reasoning
Students come to realizations—“a-ha” moments is a good term for this— about the math operations that they are performing
and use this knowledge in subsequent problems. There are plenty of these moments in fifth
grade, especially because of the emphasis on fractions and decimals. For example, with
an equation such as 90 x 0.11, students might recognize that 0.11 is about equivalent
to 1/9. When solving the problem via an algorithm, they might already know the solution
will be around 10 (9.9, to be exact) and realize a problem exists if their answer is
nowhere near what they initially concluded.

How to Help Your Children Succeed Beyond CCSS

Some of parents’ trepidation with Common Core isn’t so much with the guidelines themselves, but with the testing now aligned
with CCSS via local math curricula. Standardized testing was stressful for students and parents
before; with the ongoing Common Core implementation, many families simply don’t know what to
expect.

Fortunately, CCSS does not have to be that stressful, for you or your fifth-grader. Here are some tips to help your children
succeed with Common Core math:

Be informed; be involved

If Common Core concerns you, intrigues you, or confuses you, don’t hesitate to learn as much about it—in your child’s classroom,
at your kids’ school, and on a national level. Talk with teachers, principals, and other parents.
Seek advice on how you can help your kids, and yourself, navigate CCSS math. If you want to take
further action, become involved with PTA or other organizations and committees that deal with
your school’s curriculum. The more you know, the more, ultimately, you can help your child.

Give them some real-world math

A basic tenet of Common Core is to apply math principles to real-world situations. Why not start now? Give your child math
problems when you are out and about—the grocery store, in traffic, the park, and so on. For example,
if you are putting gasoline into your car, before you start dispensing the fuel, ask your fifth-grader
how much money will be required to fill up your 15-gallon tank. Without a pencil and notebook
to compute the answer, he or she might have to fall back on alternative math processes— processes
that Common Core encourages—for a solution.

Take time to learn what they are learning

You might look at a worksheet your child brings home and think, “This isn’t the math I’m used to.” Because Common Core emphasizes
understanding the process of arriving at an answer, your child may be taught additional ways
to fry a mathematical egg, so to speak. Instead of shunning these approaches, learn them for
yourself. Once you comprehend these additional methods, you will be better able to help your
child comprehend them as well.

Encourage them to show their work

This suggestion can be read two ways. First, students will be encouraged to show how they arrived at an answer (and beginning
with fifth-grade math, some answers can be self-checked to see if they are correct), especially
within Common Core. Second, ask your children to show you their homework, particularly the challenging
stuff. Explaining how a problem is solved is a basic CCSS tenet, so if your kids can be confident
in explaining their work to you, they will carry that confidence into the classroom when the
teacher asks for those same explanations.

Seek more help if necessary

If your fifth-grader is struggling with the new math standards, talk with his or her teacher first. You then might want to
seek outside resources to help your child. Several online resources provide math help, including
worksheets and sample tests that conform to Common Core standards. Tutoring might be an option
you consider as well. Innovative iPad based math programs have emerged that combine the personalized
approach of a tutor with today’s technology. This revolutionary approach also may feature a curriculum
based on Common Core, thus ensuring your child’s learning at home is aligned with what he or
she is learning at school.

Math Practice Worksheets

Operations and Algebraic Thinking

Which expression does the image represent?

4 × (5 × 3)

3 × (2 × 5)

4 × (2 × 3)

2 × (5 × 3)

There are 50 hens in a farm. One-fourths of the hens are white. One-tenths of the hens
are brown. Identify the expression that denotes the sum of white and brown hens in
the farm.

50/4 + 1/10

1/4 + 1/10

1/4 + 50/10

50/4 + 50/10

David writes the expression 45/{20 - 11}. Which of the following represents one-fifths
of David’s expression?

45 x 5/20 - 11

45/5(20 - 11)

20 - 11/45x45

5/45(20 - 11)

Fill in the missing number

8, 40, 44, 220, 224, ___

Fill in the missing number

13, 52, 48, 192, 188, ___

Evaluate the expressions

9 + 2 x 14 = ___

(9 + 2) x 14 = ___

Simplify the expression

52 - (25 ÷ 5 x 5 + 12)

Write the expression for:
Seven more than the quotient of ninety six divided by twelve

(7 + 96) ÷ 12

7 + (96 ÷ 12)

7 ÷ 96 + 12

96 + 12 ÷ 7

Identify the correct description: (60 - 14) ÷ 23

Difference of sixty and the product of fourteen and twenty three

Quotient of the difference of sixty and fourteen divided by twenty three

Quotient of twenty three divided by the difference of sixty and fourteen

Quotient of sixty divided by fourteen added to twenty three

Write the expression for:
One-third the size of the product of four and three

3 × 4 × 3

1/3 + 4 x 3

1/3 + 4 - 3

1/3 x 4 x 3

Number Operations in Base 10

Fill in the missing number
__ ten thousands = 7 hundred thousands

7

10

70

100

Is the statement true or false?
The digit ‘3’ in 30,576 is ten times greater than the ‘3’ in 93,678.

True

False

Mrs. Paul asked her children to compare the numbers 7,289.45 and 6,273.84. The value
of 4 in 7,289.45 is _ times greater than in 6,273.84.

A distant star in our galaxy is 10,000,000 miles away from the Earth. What is this distance
in exponential form?

10 × 10
8 miles

10 × 10
7 miles

1 × 10
6 miles

1 × 10
7 miles

Solve: _ × 10⁴ = 67,900

Select the correct option 6,590 ÷ 10
2

6,590

65.9

0.6590

I have 491 roses. How many bouquets of 19 roses can I make?

435 balloons were blown for 34 birthday parties. Each party had 30 guests. If the balloons
were distributed equally, each party would have ___ balloons and ___ balloons would
remain.

Ashley gave a set of earrings and bangles to 4 of her friends. If earrings cost her $50
and bangles cost her $38, how much money did she spend in all?

Round off 0.552 to the nearest tenths

Numbers and Operations: Fractions

Select the option that will make the statement true: 3/5 x 4/3 ___4/3

>

<

=

Convert the given fraction to mixed fraction: 10/7 = 1 __/7

8/3 - 8/5

Natasha has 48 Math problems to solve. She does 2/8 of the problems in the morning
and 4/8 of the problems in the evening. How many problems are left for her to
do?

4/21 of 6/40

Fill in the blanks: 16 x 5/__ = 10

Dickson built two tanks and asked Jason and Alex to fill each tank with water. The
extent to which they filled the tank is shown.
Is the statement “Jason’s tank is filled with more water than Alex’s” true or
false?

True

False

Mom cuts 2 pizzas, each into 8 equal pieces. Ryan ate 4 pieces, William ate 3 pieces,
and Ashley ate 2. What fraction denotes the total portion that was eaten?.

The area of each tile is square inches. What is the area of the rectangle in square
inches?

As a part of her fitness plan, Cathy has to run 4 kilometers. If she runs kilometer
in a minute, how long will she take to run 4 kilometers?

Measurement and Data

Given 1 kL = 1000 L,
68 L = __ kL

97.861 km = __ km __ m

The train covered 225 km 550 m in the first hour, 230 km 650 m in the second hour and
210 km 900 m in the third hour. How much distance did the train cover in these three
hours?
___ km ___ m

David is packing packets of cookies into a carton. Which of these dimensions would he
need to find the number of cartons that he has to buy?

Length of the carton

Height of the carton

Number of packets of cookies

Width of the carton

Fill in the missing number: The figure has _ cubes.

Select the option that makes the statement true: If both shapes are made of equal-sized
unit cubes, Volume of A ____ Volume of B.

>

<

=

The side of each small cube measures 1 in. What is the area (in sq. in.) of the base of the large box?

The volume of the combined prism is 600 cu. in. If the volume of Prism A is 180 cu. in., what is the height (in inches) of
Prism B?

Sue and her friends string beads to decorate a Christmas tree. The line plot shows
the lengths (in inches) of the beads they string. What is the combined length,
in inches, of all the beads that they used?

Which of the plots represents the data in the table? (Scroll down to see all options)
The chart gives the number of teaspoons of yeast that Mom used to make bread
every day in the month of April.

Geometry

What are the co-ordinates of D?

(4, 4)

(4, 5)

(5, 4)

(0, 4)

The co-ordinates of P are (2, -3). Is the statement true or false?

True

False

Jake starts at (5, 0) and moves 5 units to the right, along the x-axis. Write the co-ordinates
of Jake’s new position.

Fiona’s house is at the point shown F on the graph. Her school is four miles to the left
of her house. Write the coordinates of her school.

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